Use the Laplace transform to solve the following initial-value problem for a second-order equation. y" - y = 12e2t, y(0) = 1 = y'(0) y(t) =

Q: Find the general solution of the following first-order ODE xy' = y + 2x3 sin?

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Q: Find y as a function of a if x?y" + 15xy + 49y = 0, |3D y(1) = -5, y'(1) = 4. y =

A: Given differential equation is  x2y''+15xy'+49y=0 given y(1)=-5,y'(1)=4

Q: Solve the ODE  y'+(1/x)y-ex=0, when x>0

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Q: Find y as a function of t if y(0) = 2, y'(0) = 5. y(t) = 100y" +9y = 0,

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Q: If tan2(2y) – S cost dt = 4 - x² %3D dx

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Q: Find the solution for this second ODE y(0) = 1, y'(0) = 1

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Q: 2x + 2y %3D 1. Use implicit differentiation to find dy/dx for ey

A: GIVEN ex2y =2x+2y

Q: y" (f) + (1 – t) y' (4) + e'y (t) = – 5t; y (0) = - 3; y' (0) = 4 into an in- tegral equation.…

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Q: Use the chain rule to help you find dy/dx for each of the following functions: 10. y = (x²+4)³ 12. y…

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Q: Solve the D.E (X+1) =x(y'い) dメ

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Q: 3. Find the derivative of y = | (12 +1) dt.

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Q: Find y' of sin(x+y)=x+y

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